Graph Algorithms for Irregular, Unstructured Data John Feo Center for Adaptive Supercomputing Software Pacific Northwest National Laboratory July, 2010

Analytic methods and applications Community thought leaders Blog Analysis Community Activities FaceBook M users Connect-the-dots Bus Hayashi Zaire Train Anthrax Money Endo National Security People, Places, & Actions Semantic Web Anomaly detection Security N-x contingency analysis SmartGrid

Data analytics Sample queries: Allegiance switching: identify entities that switch communities. Community structure: identify the genesis and dissipation of communities Phase change: identify significant change in the network structure Traditional graph partitioning often fails: Topology: Interaction graph is low-diameter and has no good separators Irregularity: Communities are not uniform in size Overlap: individuals are members of one or more communities 1000x growth in 3 years! has more than 300 million active users

Graphs are not grids Graphs arising in informatics are very different from the grids used in scientific computing Static or slowly involving Planar Nearest neighbor communication Work performed per cell or node Work modifies local data Scientific Grids Dynamic Non-planar Communications are non-local and dynamic Work performed by crawlers or autonomous agents Work modifies data in many places Graphs for Data Informatics

Small-world and scale-free In low diameter graphs work explodes difficult to partition high percentage of nodes are visited “Six degrees of separation” Large hubs are in grey In scale-free graphs difficult to partition work concentrates in a few nodes

Paths Shortest path Betweenness Min/max flow Structures Spanning trees Connected components Graph isomorphism Groups Matching/Coloring Partitioning Equivalence Graph methods Influential Factors Degree distribution Normal Scale-free Planar or non-planar Static or dynamic Weighted or unweighted Weight distribution Typed or untyped edges Load imbalance Non-planar Concurrent inserts and deletions Difficult to partition

Challenges Problem size Ton of bytes, not ton of flops Little data locality Have only parallelism to tolerate latencies Low computation to communication ratio Single word access Threads limited by loads and stores Frequent synchronization Node, edge, record Work tends to be dynamic and imbalanced Let any processor execute any thread

Grids, Uniform, and Scale-Free Graphs USA Roadmap Uniform Scale-Free METIS Partitioner

System requirements Global shared memory No simple data partitions Local storage for thread private data Network support for single word accesses Transfer multiple words when locality exists Multi-threaded processors Hide latency with parallelism Single cycle context switching Multiple outstanding loads and stores per thread Full-and-empty bits Efficient synchronization Wait in memory Message driven operations Dynamic work queues Hardware support for thread migration Cray XMT

Center for Adaptive Supercomputer Software Driving Development of Next-Generation Massively Multithreading Architectures Sponsored by DOD

Summary The new HPC is irregular and sparse There are commercial and consumer applications If the applications are important enough, machines will be built HPC is too large and too diverse for “one size fits all” We need to build the right machines for the problems we have to solve